Open boundary conditions of the $D_3^{(2)}$ spin chain and sectors of conformal field theories

We study open boundary conditions for the $D_3^{(2)}$ spin chain, which shares connections with the six-vertex model, under staggering, and also to the antiferromagnetic Potts model. By formulating a suitable transfer matrix that is related to $K$ matrices and to the Jimbo $R$-matrix, we obtain an analytical expression for the Hamiltonian, as a logarithmic derivative of the transfer matrix, under open boundary conditions. Such computations have connections with several objects studied in Integrable Probability, which underlie exactly solvable structures.